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SCIENCE 



[N. S. Vol. XXXVII. No. 943 



turn theory, since it modifies classical 

 theory only in the assumption of discon- 

 tinuities in time, but not in space, in the 

 emission (not in the absorption) of radiant 

 energy. 



When we lay aside all consideration of 

 the origin of this theory, and ask for its 

 experimental credentials, we find two great 

 successes commonly attributed to it, (1) it 

 gives a correct energy-distribution curve; 

 (2) it enabled Planck to deduce from radi- 

 ation constants a value of the elementary 

 electrical charge which agrees within its 

 own limits of uncertainty — about 4 per 

 cent. — with the values obtained by other 

 and more accurate methods. The firet of 

 these claims is apparently justified, though 

 too much stress must not be laid upon it in 

 view of, first, the origin of the equation, 

 and, second, the fact that from the short- 

 est observable wave-lengths, clear down to 

 the longest visible red, Wien's equation 

 also fits the facts perfectly for all tempera- 

 tures up to those of the arc. In other 

 words, from the experimentalist's stand- 

 point Planck's equation may be considered 

 as Wien's equation with but a small cor- 

 rection term applied to it at one end. Such 

 correction terms can often be obtained 

 from a great variety of assumptions. 



The second claim can not be considered 

 at all, since the deduction of the value of e 

 from the radiation constants has nothing 

 whatsoever to do with quantum theory. 

 The result comes just as well from Ray- 

 leigh 's equation^* as from Planck 's and the 

 significance of the fact that the correct 

 value of e is obtained is that for certain 

 ranges of temperature the kinetic energy 

 of an oscillator in equilibrium with a gas 

 is indeed the same as the translational 

 kinetic energy of a gas molecule. Further 

 successes of Planck's theory will be con- 

 " Einstein, Ann. der Phys., 17, p. ]32, 1905. 



sidered after the discussion of the other 

 atomistic theories of radiation. 



2. The second of these theories is some- 

 what more radical than the first, and is, in 

 fact, merely that originally proposed by 

 Planck. It assumes that both emissions and 

 absorption of energy are discontinuous in 

 time. Despite the fact that Planck has re- 

 nounced this point of view, the theory re- 

 fuses to die. Nernst and most of the in- 

 vestigators who are working in specific heat 

 relations still adhere to it. What is the ex- 

 perimental situation which seems to de- 

 mand it? It is a situation brought about 

 by the recent development of methods of 

 studjnng specific heats at high and low tem- 

 peratures. I refer especially to the licjue- 

 faction of hydrogen and helium. Let us 

 consider first the simplest case, namely, 

 that of the specific heats of gases. 



One of the most brilliant triumphs of the 

 kinetic theory was the prediction that the 

 molecular heat of a monatomic gas should 

 be 2.98 calories, or approximately 1 calorie 

 per degree of freedom of the molecule, a 

 prediction accurately verified by experi- 

 ment. Next, the theory said that the 

 molecular heat of a more complex gas 

 should be as many calories as its molecule 

 has degrees of freedom. If then the mole- 

 cule of a diatomic gas acts like a rigid 

 frictionless dumbbell, no energy whatever 

 going into vibrations along the line of con- 

 nection of its two atoms, or into rotations 

 about this line as an axis, then its degrees 

 of freedom should be three translational, 

 and two rotational, and hence its molecu- 

 lar heat should be 5 calories, which is, as a 

 matter of fact, the value found for all of 

 the so-called permanent diatomic gases at 

 ordinary temperatures. 



Now, however, come the facts which call 

 for some modification of the simple dynam- 

 ical theory. , We have long known that 

 even at ordinary temperatures the molec- 



